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A239623 Conjecturally, the largest k such that prime(n)^2 is the largest squared prime divisor of binomial(2k,k).

%I A239623 #14 Mar 14 2015 00:41:51
%S A239623 4,786,785,2080,902,2034,2079,1086,2081,2090,1652,2562,3905,8185,4987,
%T A239623 3507,5562,2713,3584,4191,8285,9319,12237,12117,12248,9311,8180,8399,
%U A239623 9308,20123,11977,11683,12261,14365,15403,20114,16867,19938,19559,20316,24706
%N A239623 Conjecturally, the largest k such that prime(n)^2 is the largest squared prime divisor of binomial(2k,k).
%C A239623 The last number in row n of A239622. The 0th term is the largest number k such that binomial(2k,k) is squarefree. The first 41 terms were checked by computing binomial(2k,k) for k <= 10^5. See the plot in A110493.
%H A239623 Vincenzo Librandi, <a href="/A239623/b239623.txt">Table of n, a(n) for n = 0..125</a>
%t A239623 b = 1; t = Table[b = b*(4 - 2/n); last = 0; Do[If[Mod[b, p^2] == 0, last = p], {p, Prime[Range[PrimePi[Sqrt[2*n]]]]}]; last, {n, 25000}]; t = Join[{0}, t]; Table[Flatten[Position[t, p]][[-1]] - 1, {p, Join[{0}, Prime[Range[20]]]}]
%Y A239623 Cf. A110493, A110494, A239622, A239624.
%K A239623 nonn
%O A239623 0,1
%A A239623 _T. D. Noe_, Mar 27 2014